A boat moves through the water with two forces acting on it. One is a 2000-N for

Question

A boat moves through the water with two forces acting on it. One is a 2000-N forward push by the water on the propeller, and the other is a 1800-N resistive force due to the water around the bow. (a) What is the acceleration of the 1000-kg boat? (b) If it starts from rest, how far will the boat move in 10.0s? (c) What will its velocity be at the end of that time? A 2-kg block is given an initial speed of 2.5 m/s up a plane inclined 15 degree with the horizontal. The coefficient of kinetic friction between block and plane is 0.250. What speed does it have just as it returns to its initial position?

Explanation / Answer

a ) Net force = 2000-1800 = 200 N

a= F/mass = 200/1000= 0.2 m/s^2

b)s= 1/2 ( 0.2)( 10)^2= 10 m

c)v= at = 0.2 ( 10 ) = 2 m/s

Q. 2 we will use conservation of energy to find the energy at top

let the height gained = h, slant distance covered = s 0,.2

1/2 mv^2 = mgh + work done to overcome friction

1/2 (m) ( 2.5^2) = ( m) (9.8 ) (h) + 0.25 ( mg cos15) ( s)

1/ 2 (6.25) = 9.8 h + 2.366 (s)

s= h/ sin 15

3.125 =18.94 h

h = 0.165 m apprx

energy at top = 2 ( 9.8) ( 0.165) = 3.234 J

3.234 J= 1/2 ( 2) v^2 + 0.25 ( 2x 9.8 x cos15) ( s) ( s= 0.165/ sin 15= 0.165/ 0.259 = 0.637 m)

v^2 = 0.219

v = 0.4679 m/s apprx

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